Z statistic

A commonly used transformation of a standard normal distribution. The resulting distribution has a mean of 0 and a standard deviation of 1. Used extensively in hypothesis testing.

Also known as the Z score.

So for example if a data point has a Z score (or Z statistic) of -1.64, then it lies 1.64 standard deviations below the mean.

The Z score is calculated as the difference between the data point (X) and the mean E[x], all divided by the standard deviation of the population (SD). For example if:

the mean (E[x]) of a population = 100;
the standard deviation (SD) = 10; and
a given observation (or data point) = 83.6;

then the Z score (Z) is calculated as:

Z = (X - E[x])/SD

= (83.6 - 100 = -16.4)/10
= - 1.64 standard deviations.

In this case the Z score is negative, indicating that the data point (83.6) lies below the mean (of 100).

See also

• Standardised normal distribution